$A$ fan rotating with an angular speed of $600 \, rev/min$ comes to rest after $60$ revolutions when switched off. The time taken to come to rest is ........ $(sec)$.

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with constant angular acceleration $\alpha$. The magnitude of the average velocity,in the time it completes a small angular displacement $\theta$,is:

The angular acceleration of a wheel is $3 \ rad/s^2$. If its initial angular velocity is $2 \ rad/s$,what is the angular displacement (in $rad$) covered by it in $2 \ s$?

$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

$A$ particle of mass $m$ moves along a circle of radius $r$ with constant tangential acceleration. If the kinetic energy $E$ of the particle becomes three times by the end of the third revolution after the beginning of the motion,then the magnitude of the tangential acceleration is:

An athlete throws a discus from rest to a final angular velocity of $15 \, rad \, s^{-1}$ in $0.270 \, s$ before releasing it. During acceleration,the discus moves along a circular arc of radius $0.810 \, m$. The acceleration of the discus before it is released is ....... $m \, s^{-2}$.